A quasilinear problem with large diffusion and nonlinear dynamic boundary conditions
Abstract
Abstract This paper concerns quasilinear parabolic equations with p-Laplacian and q-Laplacian–Beltrami principal operators, subject to nonlinear dynamic boundary conditions. We examine the effect of large diffusion on the system, which leads to spatial homogenization. We establish the well-posedness of the perturbed problem and prove that, as the diffusion coefficients become large, the solution converges to that of a limiting system of ordinary differential equations. Additionally, we demonstrate the upper semicontinuity of the attractors, showing their converge to the limiting attractor as the parameter $$\varepsilon $$ ε tends to zero.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Stability and Controllability of Differential Equations
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Journal of Elliptic and Parabolic Equations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 12
- Issue
- 1
- Pages
- 1277–1295
- Publication date
- 10 April 2026
- Language
- EN